On influence of substrate compliance on delamination and buckling of coatings

Abstract

Abstract. Problems related to delamination of coatings from substrates and their buckling are widely investigated due to importance of the problem for application in industry, particularly in micro-and nano-electronics and biology. The problem was addressed by many authors by using both analytical and numerical approaches. Here the model is developed that treats the delaminated part of the coating as a plate with a special attention given to the boundary conditions, which are supposed in the form of the generalized elastic clamping, i.e. it is supposed that components of displacements and angle of rotation at the point of clamping are related to the acting total force and total moment by means of 3x3 matrix of elastic coefficients. Knowing the coefficients of this matrix allows determining parameters of buckling such as the critical stress, energy release rate due to further delamination, amplitude of buckling. A few variants of analytical models to determine the coefficients of this 3x3 matrix were considered and discussed. Both the cases of isotropic and anisotropic coating and substrate are considered. The solution for some matrix coefficients was obtained with the help of Fourier transform and WienerHopf technique. On the base of the obtained solution it is shown that the difference between the obtained critical stress and the critical stress of a rigidly clamped plate can be defined by a single nondimensional parameter, which is a combination of the elastic constants of the coating and substrate, and the ratio of delamination length to coating thickness. The results correlate well with the results obtained using the FEM model. IntroductionThe interest to effects, related to coatings delaminations causes by importance of the problem for such fields as micro-and nanoelectronics, biology, medicine. Number of studies is devoted to the problem e.g. , and energy release rates along and across the delamination front as well were found. The delaminated part of coating was considered as a clamped plate, which corresponds to rigid substrates. However, detailed studies yield that, from the one hand, the condition of rigid clamping are not satisfied exactly even for absolutely rigid substrates [5], and, from the other hand, on the base of numerical calculations it is said [6], [7] that even for substrates tree times softer then coating the condition of rigid clamping yields acceptable errors. The last statement has to be accepted with cautions, because the influence of delamination size, importance of which being confirmed by other studies [5], [8], was not investigated in [6]. Influence of the substrate rigidity was studied by [4][5][6], however without paying attention to the influence of the delamination width to the critical stress. The analysis of influence of both substrate compliance and delamination width on the critical stress was performed in [5]. The delamination

Nacre‐Inspired, Liquid Metal‐Based Ultrasensitive Electronic Skin by Spatially Regulated Cracking Strategy

“…Second, the formation of bucklings is considered to be induced by compressive strain in the metallic film coupled to the soft substrates. [56][57][58] Although bucklings can be observed in both the patterned and the unpatterned Ag film (Figure 1c,d), the patterned group exhibited more bucklings with higher line density (≈0.05 µm −1 vs ≈0.03 µm −1 under 50% strain). As demonstrated in Figure S11, Supporting Information, this phenomenon is mainly due to the more lateral compressive strain in B-marked Ag region than in unpatterned Ag film.…”

Fracture Mechanics Solutions for Interfacial Cracks between Compressible Thin Layers and Substrates

“…The effect is important for stiff layers over soft substrates, where the function f V becomes very large (Figure 3b and Table 5). In the absence of shear, the root rotations due to pure bending would not have any effects on the fracture parameters [25], but only on the deformability of the system, e.g., in buckle-driven delamination [15,16,54]. These concepts have recently been discussed in [55] for sandwich beams and in [56] for bi-material DCB specimens.…”

On delamination of bi‐layers composed by orthotropic materials: Exact analytical solutions for some particular cases

“…Therefore, the essential part of stress state is totally determined by four force parameters. Keeping in mind the method to be used [1, 3, 19], following [1] the four independent parameters will be chosen in terms of integral values of stresses acting along the intact part of the interface, …”

“…three and four point bending; studying fracture processes in layered structures [5–13]; studying delamination of thermal and environmental coatings [14–16]. Propagation of interface cracks was also studied in context of indentation of layered structures [17], processes of buckling [6, 18–20], for interpreting results of blister tests [21, 22].…”